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CALCULUS AND ANALYSIS
DIFFERENTIAL EQUATIONS
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Recent Differential equations Answers
Recent questions in Differential equations
First order differential equations
asked 2021-03-02
Solve differential equation
\(ty'+(t+1)y=t, y(ln 2)=1\)
, t>0
First order differential equations
asked 2021-03-02
Solve the differential equation
\((x-3y)dx-xdy=0\)
First order differential equations
asked 2021-03-02
Transform the given initial value problem into an initial value problem for two first-order quations
\(u"+0.25u'+4u=2cos(3t)\)
, u(0)= 1, u'(0)= -2
First order differential equations
asked 2021-03-01
Solve differential equation
\(t^2dy= (8ln^2t-ty)dt\)
Laplace transform
asked 2021-02-26
Solve the following initial value problems using Laplace Transforms:
\(\displaystyle\frac{{{d}^{2}{y}}}{{{\left.{d}{x}\right.}^{2}}}+{25}{y}={t}\)
\(y(0)=0\)
\(y'(0)=0.04\)
Laplace transform
asked 2021-02-26
How many poles does the Laplace Transform of a square wave have?
a) 0
b) 1
c) 2
d) Infinitely Manhy
Differential equations
asked 2021-02-26
Make and solve the given equation
\(x\ dx\ +\ y\ dy=a^{2}\frac{x\ dy\ -\ y\ dx}{x^{2}\ +\ y^{2}}\)
First order differential equations
asked 2021-02-25
Solve differential equation
\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}+{\frac{{{y}}}{{{4}{x}}}}={3}{x},\ {y}{\left({2}\right)}={3}\)
Second order linear equations
asked 2021-02-25
Solve the linear equations by considering y as a function of x, that is, y = y(x).
\(\displaystyle\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}-{y}={4}{e}^{x},{y}{\left({0}\right)}={4}\)
Laplace transform
asked 2021-02-25
Use properties of the Laplace transform to answer the following
(a) If
\(f(t)=(t+5)^2+t^2e^{5t}\)
, find the Laplace transform,
\(L[f(t)] = F(s)\)
.
(b) If
\(f(t) = 2e^{-t}\cos(3t+\frac{\pi}{4})\)
, find the Laplace transform,
\(L[f(t)] = F(s)\)
. HINT:
\(\cos(\alpha + \beta) = \cos(\alpha)\cos(\beta) - \sin(\alpha) \sin(\beta)\)
(c) If
\(F(s) = \frac{7s^2-37s+64}{s(s^2-8s+16)}\)
find the inverse Laplace transform,
\(L^{-1}|F(s)| = f(t)\)
(d) If
\(F(s) = e^{-7s}(\frac{1}{s}+\frac{s}{s^2+1})\)
, find the inverse Laplace transform,
\(L^{-1}[F(s)] = f(t)\)
Laplace transform
asked 2021-02-25
Solve no.4 inverse laplace
\(L^{-1}\left\{s \ln\left(\frac{s}{\sqrt{s^2+1}}\right)+\cot^{-1s}\right\}\)
Differential equations
asked 2021-02-25
Give the correct answer and solve the given equation:
\(\displaystyle{y}\ \text{ - 4y}+{3}{y}={x},{y}_{{1}}={e}^{x}\)
Laplace transform
asked 2021-02-24
For the function
\(f(t)=e^t\)
\(g(t)=e^{-2t}\)
\(0\leq t < \infty\)
compute in two different ways:
a) By directly evaluating the integral in the defination of
\(f \cdot g\)
b) By computing
\(L^{-1}\left\{F(s)G(s)\right\} \text{ where } F(s)=L\left\{f(t)\right\} \text{ and } G(s)=L\left\{g(t)\right\}\)
Second order linear equations
asked 2021-02-24
Solve the linear equations by considering y as a function of x, that is, y = y(x).
\(\displaystyle\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}+{\left(\frac{1}{{x}}\right)}{y}={x}\)
Laplace transform
asked 2021-02-24
determine the inverse Laplace transform of F.
\(F(s)=\frac{e^{-2s}}{(s-3)^3}\)
Laplace transform
asked 2021-02-24
What would be the laplace transform of a function of f or
\(L\left\{f(t)\right\}\)
?
First order differential equations
asked 2021-02-24
Solve the differential equation
\(x dy/dx= y+xe^(y/x)\)
, y=vx
First order differential equations
asked 2021-02-24
Solve differential equation
\((x+2)y′+4y=(3x + 6)^-2 lnx\)
First order differential equations
asked 2021-02-23
Solve differential equation
\(dy/dx+ycos(x)= 4cos(x)\)
, y(0)=6
First order differential equations
asked 2021-02-21
Solve differential equation
\(\displaystyle{y}'+{3}{x}^{{2}}{y}={\sin{{\left({x}\right)}}}{e}^{{-{x}^{{3}}}},\ {y}{\left({0}\right)}={1}\)
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